The base of a triangular garden is 5 yards longer than the​ height, and the area of the garden is 168 square yards. Find the dimensions of the triangle?

word problems

2 Answers
Nov 7, 2017

height= 16 yards
base = 21 yards

Explanation:

Let the height of the triangular shaped garden be h yards. Its base would then be 5+h yards.

Formula for the area of any traingle is 1/2 base X height.

By this formula, 1/2 (5+h) Xh= 168

On simplifying this. h^2 +5h =336

Or h^2 +5h-336=0. Now factorise this quadratic expression by splitting the middle term, keeping in view the fact that 21X16=336 and difference 21-16 =5. This would be as follows:

h^2 +21h -16h -336=0. Now pair these terms,

(h^2 +21h) -(16h +336)=0
h(h+21) -16(h+21)=0

(h+21)(h-16)=0. This means either h-16=0 or h+21=0.

Since h+21=0 would mean h= -21, this cannot be the required solution, because height of the triangle can never be negative. Hence, h-16=0 would give the height of the triangle as h= 16 yards. The dimensions of the triangle would be height = 16 yards and length of the base = 21 yards
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Nov 7, 2017

"base "=21" yards and height "=16" yards"

Explanation:

"let the height "=h

"then base "=h+5larrcolor(blue)"5 yards longer"

• " area of triangle "=1/2" base "xx"height"

rArr1/2h(h+5)=168

"multiply both sides by 2"

rArrh(h+5)=336

"express in standard form and factorise"

rArrh^2+5h-336=0larrcolor(blue)"in standard form"

"the factors of - 336 which sum to + 5 are + 21 and - 16"

rArr(h+21)(h-16)=0

"equate each factor to zero and solve for h"

h+21=0rArrh=-21larrcolor(red)"not valid"

h-16=0rArrh=16

"since "h>0" then h = 16"

"base of triangle "=h+5=16+5=21" yards"

"and height "=h=16" yards"

color(blue)"As a check"

"area "=1/2bh=1/2xx21xx16=168" square yards"